Automatic Control Systems
If any term in the first column of a Routh array becomes zero, then

Routh criterion can be used by substituting a small negative number for zero and complet-ing the array
Routh criterion can be used by substituting a small positive number for zero and completing the array
Routh criterion cannot be used to determine stability
Routh criterion can be used by substituting a big positive number for zero and completing the array

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